An Isogeometric One-Dimensional Model for Developable Flexible Elastic Strips

This paper aims at introducing a kinematical reduction for Kirchhoff-Love shells with developable base surfaces that undergo isometric deformations. This framework is appropriate to model, for example, flexible flat cables. In order to decrease the involved number of degrees of freedom, we utilise kinematical reduction to a geodesic line and a vector field along this curve. Application of a relatively parallel frame allows us to generalise this framework to a more general class of curves that may exhibit points or segments of vanishing curvature. We derive the one-dimensional bending energy functional for a rectangular strip, combine it with penalty terms addressing the nonlinear constraints, and compute the equilibrium state as minimiser of this penalised energy. An isogeometric discretisation yields finitely many degrees of freedom for the inner point optimiser. Several example strips clamped at both ends illustrate the feasibility of this approach.